Topic/Skill Definition/Tips
Topic: Systematic Listing Example
1. A collection of things, where the order How many combinations of two
Combination does not matter. ingredients can you make with apple,
banana and cherry?
Apple, Banana
Apple, Cherry
Banana, Cherry
3 combinations
2. Permutation A collection of things, where the order You want to visit the homes of three
does matter. friends, Alex (A), Betty (B) and
Chandra (C) but haven’t decided the
order. What choices do you have?
ABC
ACB
BAC
BCA
CAB
CBA
3. When something has n different types, How many permutations are there for a
Permutations there are n choices each time. three-number combination lock?
with
Repetition Choosing r of something that has n 10 numbers to choose from
different types, the permutations are: {1 , 2 , ….10 } and we choose 3 of them
3
n × n× … ¿ 10 ×10 ×10=10 =1000 permutations.
4. We have to reduce the number of How many ways can you order 4
Permutations available choices each time. numbered balls?
without
Repetition One you have chosen something, you 4 ×3 ×2 ×1=24
cannot choose it again.
5. Factorial The factorial symbol ‘!’ means to multiply 4 !=4 × 3× 2× 1=24
a series of descending integers to 1.
Note: 0 !=1
6. Product If there are x ways of doing something and To choose one of { A , B ,C } and one of
Rule for y ways of doing something else, then there { X ,Y } means to choose one of
Counting are xy ways of performing both. { AX , AY , BX , BY ,CX ,CY }
The rule says that there are 3 ×2=6
choices.
Mr A. Coleman Glyn School
Topic: Systematic Listing Example
1. A collection of things, where the order How many combinations of two
Combination does not matter. ingredients can you make with apple,
banana and cherry?
Apple, Banana
Apple, Cherry
Banana, Cherry
3 combinations
2. Permutation A collection of things, where the order You want to visit the homes of three
does matter. friends, Alex (A), Betty (B) and
Chandra (C) but haven’t decided the
order. What choices do you have?
ABC
ACB
BAC
BCA
CAB
CBA
3. When something has n different types, How many permutations are there for a
Permutations there are n choices each time. three-number combination lock?
with
Repetition Choosing r of something that has n 10 numbers to choose from
different types, the permutations are: {1 , 2 , ….10 } and we choose 3 of them
3
n × n× … ¿ 10 ×10 ×10=10 =1000 permutations.
4. We have to reduce the number of How many ways can you order 4
Permutations available choices each time. numbered balls?
without
Repetition One you have chosen something, you 4 ×3 ×2 ×1=24
cannot choose it again.
5. Factorial The factorial symbol ‘!’ means to multiply 4 !=4 × 3× 2× 1=24
a series of descending integers to 1.
Note: 0 !=1
6. Product If there are x ways of doing something and To choose one of { A , B ,C } and one of
Rule for y ways of doing something else, then there { X ,Y } means to choose one of
Counting are xy ways of performing both. { AX , AY , BX , BY ,CX ,CY }
The rule says that there are 3 ×2=6
choices.
Mr A. Coleman Glyn School
